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first order logic

Is business logic too much for classical logic?

Business logic is not limited to mathematical logic, as in first-order predicate calculus.

Business logic commonly requires “aggregation” over sets of things, like summing the value of claims against a property to subtract it from the value of that property in order to determine the equity of the owner of that property.

  • The equity of the owner of a property in the property is the excess of the value of the property over the value of claims against it.

There are various ways of describing such extended forms of classical logic.  The most relevant to most enterprises is the relational algebra perspective, which is the base for relational databases and SQL.  Another is the notion of generalized quantifiers.

In either case, it is a practical matter to be able to capture such logic in a rigorous manner.  The example below shows how that can be accomplished using English, producing the following axiom in extended logic:

  • ∀(?x15)(property(?x15)→∀(?x10)(owner(of)(?x10,?x15)→∃(?x31)(value(of(?x15))(?x31)∧∑(?x44)(∀(?x49)(claim(against(?x15))(?x49)→value(of(?x49))(?x44))→∃(?x26)(excess(of(?x31))(over(?x44))(?x26)∧equity(in(?x15))(of(?x10))(?x26))))))

This logic can be realized in various ways, depending on the deployment platform, such as: (more…)

Simply Logical English

This is not all that simple of an article, but it walks you through, from start to finish, how we get from English to logic. In particular, it shows how English sentences can be directly translated into formal logic for use with in automated reasoning with theorem provers, logic programs as simple as Prolog, and even into production rule systems.

There is a section in the middle that is a bit technical about the relationship between full logic and more limited systems (e.g., Prolog or production rule systems). You don’t have to appreciate the details, but we include them to avoid the impression of hand-waving

The examples here are trivial. You can find many and more complex examples throughout Automata’s web site.

Consider the sentence, “A cell has a nucleus.”:

(more…)

Requirements for Logical Reasoning

Here is a graphic on how various reasoning technologies fit the practical requirements for reasoning discussed below:

This proved surprisingly controversial during correspondence with colleagues from the Vulcan work on SILK and its evolution at http://www.coherentknowledge.com.

The requirements that motivated this were the following: (more…)

Semantic Technology & Business Conference (SemTechBiz)

Benjamin Grosof and I will be presenting the following review of recent work at Vulcan towards Digital Aristotle as part of Project Halo at SemTechBiz in San Francisco the first week of June.

Acquiring deep knowledge from text

We show how users can rapidly specify large bodies of deep logical knowledge starting from practically unconstrained natural language text.

English sentences are semi-automatically interpreted into  predicate calculus formulas, and logic programs in SILK, an expressive knowledge representation (KR) and reasoning system which tolerates practically inevitable logical inconsistencies arising in large knowledge bases acquired from and maintained by distributed users possessing varying linguistic and semantic skill sets who collaboratively disambiguate grammar, logical quantification and scope, co-references, and word senses.

The resulting logic is generated as Rulelog, a draft standard under W3C Rule Interchange Format’s Framework for Logical Dialects, and relies on SILK’s support for FOL-like formulas, polynomial-time inference, and exceptions to answer questions such as those found in advanced placement exams.

We present a case study in understanding cell biology based on a first-year college level textbook.

Logic from the English of Science, Government, and Business

Our software is translating even long and complicated sentences from regulations to textbooks into formal logic (i.e,, not necessarily first-order logic, but more general predicate calculus).   As you can see below, we can translate this understanding into various logical formalisms including defeasible first-order logic, which we are applying in Vulcan’s Project Halo.  This includes classical first-order logic and related standards such as RIF or SBVR, as well as building or extending an ontology or description logic (e.g., OWL-DL).

We’re excited about these capabilities in various applications, such as in advancing science and education at Vulcan and formally understanding, analyzing and automating policy and regulations in enterprises.

English translated into predicate calculus

English translated into predicate calculus

a sentence understood by Automata

an unambiguously, formally understood sentence


English translated into SILK and Prolog

English translated into SILK and Prolog

Simple problems with the semantic web

The standard for defining ontologies these days is OWL and Protege.  Unfortunately, OWL lacks any notion of exceptions in inheritance or any other notion of defeasibility.

So, although you may want to say that birds fly, you’re ontology will be broken (or become much more complicated) when you realize there are birds that can’t fly, such as penguins or ostriches, or even sick or injured birds.

Practically speaking, you need something like courteous logic or the defeasibility in SILK to handle this (or any 1980s expert system shell or even earlier frame system).  OWL is very hard on mortal man (e.g., mainstream IT) in this regard.

How can I tell OWL that a pronoun is a noun but that pronouns are a closed class of words, unlike nouns, verbs, adjectives, and adverbs (in general).  Well, I’ll have to tell it about open-class nouns versus closed class nouns.  What a pain!

This is why we use Protege primarily as a drafting tool and, for example, SILK, to do reasoning.   Non-defeasible description logic and first-order reasoners are difficult to get along with, in practice (and make sustainable knowledge repositories too difficult – which inhibits adoption, obviously).

Cyc is more than encyclopedic

I had the pleasure of visiting with some fine folks at Cycorp in Austin, Texas recently.  Cycorp is interesting for many reasons, but chiefly because they have expended more effort developing a deeper model of common world knowledge than any other group on the planet.  They are different from current semantic web startups.  Unlike Metaweb‘s Freebase, for example, Cycorp is defining the common sense logic of the world, not just populating databases (which is an unjust simplification of what Freebase is doing, but is proportionally fair when comparing their ontological schemata to Cyc’s knowledge).  Not only does Cyc have the largest and most practical ontology on earth, they have almost incomprehensible numbers of formulas[1] describing the world.   (more…)